Asst. Professor, Mathematics, School of Engineering, Coimbatore

Qualification:

Ph.D, MPhil, MSc

j_geetha@cb.amrita.edu

Dr. Geetha J. currently serves as Assistant Professor (Sr. Gr.) at the department of Mathematics, School of Engineering, Coimbatore Campus. Her research interests include Graph Theory and Linear Algebra. Geetha has completed M. Sc and M. Phil in Mathematics.

**Project Title: Total coloring conjecture for certain classes of graphs****Role:**CO-PI**Duration:**2014-2016**Funding Agency:**National Board for Higher Mathematics (NBHM)**Project Title: Behzad-Vizing Conjecture on Graph Coloring for Product Graphs****Role:**CO-PI**Duration:**2015-2018**Funding Agency:**Department of Science & Technology - DST**Project Title: Total Colorings for Certain Classes of Cayley Graphs****Role:**PI**Funding Agency:**DST-SERB

Year of Publication | Title |
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2018 |
R Vignesh, Geetha, J., and Dr. Somasundaram K., “Total Coloring Conjecture for Certain Classes of Graphs”, Algorithms, vol. 11, p. 161, 2018.[Abstract] A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements receive the same color. The total chromatic number of a graph G, denoted by , is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph G, , where is the maximum degree of G. In this paper, we prove the total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph. More »» |

2018 |
J. Geetha and Dr. Somasundaram K., “Total Colorings of Product Graphs”, Graphs and Combinatorics (2018), vol. 34, no. 2, pp. 339–347, 2018.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove Behzad–Vizing conjecture for product graphs. In particular, we obtain the tight bound for certain classes of graphs. More »» |

2017 |
S. Mohan, Geetha, J., and Dr. Somasundaram K., “Total coloring of the corona product of two graphs”, AUSTRALASIAN JOURNAL OF COMBINATORICS, vol. 68, no. 1, pp. 15–22, 2017.[Abstract] A total coloring of a graph is an assignment of colors to all the elements (vertices and edges) of the graph such that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the corona product of two graphs G and H, when H is a cycle, a complete graph or a bipartite graph. More »» |

2016 |
S. Mohan, Geetha, J., and Dr. Somasundaram K., “Total Coloring of Certain Classes of Product Graphs”, Electronic Notes in Discrete Mathematics, vol. 53, pp. 173 - 180, 2016.[Abstract] Abstract A total coloring of a graph is an assignment of colors to all the elements of the graph such that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of Behzad and Vizing conjecture on total coloring for Compound graph of G and H, where G and H are any graphs. More »» |

2016 |
J. Geetha and Dr. Somasundaram K., “Total Chromatic Number and Some Topological Indices”, Electronic Notes in Discrete Mathematics, vol. 53, pp. 363 - 371, 2016.[Abstract] Abstract The total chromatic number χ ″ ( G ) of G is the smallest number of colors needed to color all elements of G in such a way that no adjacent or incident elements get the same color. The harmonic index H ( G ) of a graph G is defined as the sum of the weights 2 d ( u ) + d ( v ) of all edges uv of G, where d ( u ) denotes the degree of the vertex u in G. In this paper, we show a relation between the total chromatic number and the harmonic index. Also, we give relations between total chromatic number and some topological indices of a graph. More »» |

2015 |
J. Geetha and Dr. Somasundaram K., “Total coloring of generalized sierpiński graphs”, Australasian Journal of Combinatorics, vol. 63, no. 1, pp. 58-69, 2015.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of the graph in such a way that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the generalized Sierpiński graphs of cycle graphs and hypercube graphs. We give a total coloring for the WK-recursive topology, which also gives the tight bound. © 2015,University of Queensland. All rights reserved. More »» |

2015 |
Aa Gupta, Geetha, J., and Dr. Somasundaram K., “Total coloring algorithm for graphs”, Applied Mathematical Sciences, vol. 9, pp. 1297-1302, 2015.[Abstract] A total coloring of a graph is an assignment of colors to all the elements of graph such that no two adjacent or incident elements receive the same color. Behzad and Vizing conjectured that for any graph G the following inequality holds: Δ(G)+1≤X′′(G)≤Δ(G)+2, where Δ(G) is the maximum degree of G. Total coloring algorithm is a NP-hard algorithm. In this paper, we give the total coloring algorithm for any graph and we discuss the complexity of the algorithm. © 2015 Aman Gupta, J. Geetha and K. Somasundaram. More »» |

Year of Publication | Title |
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2015 |
J. Geetha and Dr. Somasundaram K., “Total Coloring for Certain Classes of Claw-free Graphs”, in International Conference on Graph Theory and its Applications, Puducherry, 2015. |

Faculty Research Interest: